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DNA TOPOLOGY: EXPERIMENTS AND ANALYSIS

DNA TOPOLOGY: EXPERIMENTS AND ANALYSIS. De Witt Sumners Department of Mathematics Florida State University Tallahassee, FL 32306 sumners@math.fsu.edu. Isomers. Using Topology in Science. SYNTHETIC KNOT. Dietrich-Buchecker & Sauvage, Ang. Chemie 28 (1989), 189. KNOT IN A PROTEIN.

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DNA TOPOLOGY: EXPERIMENTS AND ANALYSIS

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  1. DNA TOPOLOGY: EXPERIMENTS AND ANALYSIS De Witt Sumners Department of Mathematics Florida State University Tallahassee, FL 32306 sumners@math.fsu.edu

  2. Isomers

  3. Using Topology in Science

  4. SYNTHETIC KNOT • Dietrich-Buchecker & Sauvage, Ang. Chemie 28 (1989), 189

  5. KNOT IN A PROTEIN J. Am. Chem. Soc. 118(1996), 8945

  6. What is Knot Theory?

  7. Knots and Catenanes

  8. Crossover Number

  9. A Knot Zoo By Robert G. Scharein http://www.pims.math.ca/knotplot/zoo/ © 2005 Jennifer K. Mann

  10. Prime and Composite Knots

  11. CHIRALITY

  12. CROSSING SIGN CONVENTION

  13. LINKING NUMBERS

  14. TWIST

  15. WRITHE & AVERAGE CROSSING NUMBER Writhe --average the sum of signed crossings over all projections (average number of crossings over all projections)

  16. LK = TW + WR

  17. LK = TW + WR

  18. LK = TW + WR

  19. DNA Replication

  20. DNA is Crowded in the Cell

  21. Radial Loop Chromosome

  22. Replication Obstruction

  23. Strand Passage Topoisomerase

  24. Strand Exchange Recombinase

  25. Enzyme Bound to DNA

  26. Topological Enzymology Mathematics: Deduce enzyme binding and mechanism from observed products

  27. Information We Seek

  28. TOPOLOGICAL ENZYMOLOGY • React circular DNA plasmids in vitro (in vivo) with purified enzyme • Gel electrophoresis to separate products (DNA knots & links) • Electron microscopy of RecA coated products • Use topology and geometry to build predictive models

  29. GEL ELECTROPHORESIS

  30. Rec A Coating Enhances EM

  31. RecA Coated DNA

  32. DNA Trefoil Knot

  33. DNA (2,13) TORUS KNOT

  34. TOPOISOMERSE AND LINKING

  35. TOPO I vs TOPO II

  36. DNA PLASMID REPLICATION

  37. Topoisomerase I ExperimentDean et al. J. Biol. Chem. 260 (1985), 4795

  38. Topoisomerase Knots

  39. Topoisomerase Knots

  40. Right and Left Hand Trefoils

  41. Torus and Square Knots

  42. Gel Mobility of DNA Knots

  43. Conclusions

  44. Crystal Structure of Topoisomerase

  45. GEL VELOCITY IDENTIFIES KNOTS

  46. Toposides--Chemotherapy Topoisomerase Replication Fork

  47. SITE-SPECIFIC RECOMBINATION

  48. Enzyme Bound to DNA

  49. DIRECT vs INVERTED REPEATS

  50. RESOLVASE SYNAPTIC COMPLEX

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